Efficient Photo-heating Algorithms in Time-dependent Photo-ionization Simulations

TL;DR

This paper introduces efficient algorithms for photo-heating calculations in time-dependent photo-ionization simulations, significantly reducing computational costs while maintaining accuracy through adaptive and asynchronous evolution methods.

Contribution

The paper presents two novel methods—adaptive time-step algorithm and asynchronous evolution—for efficient and accurate photo-heating calculations in photo-ionization simulations.

Findings

Methods reduce computational cost substantially.

Algorithms maintain accuracy in cosmological tests.

Validated against existing photo-ionization code.

Abstract

We present an extension to the time-dependent photo-ionization code C$^2$-Ray to calculate photo-heating in an efficient and accurate way. In C$^2$-Ray, the thermal calculation demands relatively small time-steps for accurate results. We describe two novel methods to reduce the computational cost associated with small time-steps, namely, an adaptive time-step algorithm and an asynchronous evolution approach. The adaptive time-step algorithm determines an optimal time-step for the next computational step. It uses a fast ray-tracing scheme to quickly locate the relevant cells for this determination and only use these cells for the calculation of the time-step. Asynchronous evolution allows different cells to evolve with different time-steps. The asynchronized clocks of the cells are synchronized at the times where outputs are produced. By only evolving cells which may require short time-steps with these short time-steps instead of imposing them to the whole grid, the computational cost of the calculation can be substantially reduced. We show that our methods work well for several cosmologically relevant test problems and validate our results by comparing to the results of another time-dependent photo-ionization code.